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Prediction of the Natural Gas Compressibility Factor by using MLP and RBF Artificial Neural Networks Cover

Prediction of the Natural Gas Compressibility Factor by using MLP and RBF Artificial Neural Networks

Open Access
|Feb 2025

Figures & Tables

Fig. 1.

Ultrasonic flow measurement principle.
Ultrasonic flow measurement principle.

Fig. 2.

Schematic diagram of the MLP-ANN.
Schematic diagram of the MLP-ANN.

Fig. 3.

Schematic diagram of the RBF-ANN.
Schematic diagram of the RBF-ANN.

Fig. 4.

Effect of the number of hidden neurons of the MLP-ANN for the LM algorithm.
Effect of the number of hidden neurons of the MLP-ANN for the LM algorithm.

Fig. 5.

Effect of the number of hidden neurons of the MLP-ANN for the SCGD algorithm.
Effect of the number of hidden neurons of the MLP-ANN for the SCGD algorithm.

Fig. 6.

Scatter plot of predicted values versus observed values for MLP-ANN.
Scatter plot of predicted values versus observed values for MLP-ANN.

Fig. 7.

Plot of predicted values versus observed values for MLP-ANN.
Plot of predicted values versus observed values for MLP-ANN.

Fig. 8.

Scatter plot of predicted values versus observed values for RBF-ANN.
Scatter plot of predicted values versus observed values for RBF-ANN.

Fig. 9.

Plot of predicted values versus observed values for RBF-ANN.
Plot of predicted values versus observed values for RBF-ANN.

Fig. 10.

Comparison of relative errors of the MLP-ANN and the RBF-ANN model.
Comparison of relative errors of the MLP-ANN and the RBF-ANN model.

Comparative analysis of LM and SCGD algorithms_

AlgorithmR2MSNERMSEMAE
LM0.990320.05810.12060.087
SCGD0.942290.09530.15430.1144

Comparison between MLP and RBF models_

Type ANNR2MSNERMSEMAE
MLP-ANN0.990320.05810.12060.087
RBF-ANN0.998990.0007290.01350.0075

Tested combination of activation functions of MLP-ANN_

Activation function hidden layerActivation function output layerR2MSNERMSEMAE
tansigtansig0.990320.05810.12060.087
tansigpurelin0.992190.38660.31090.2363
logsigtansig0.944380.10340.16070.1072
logsigpurelin0.980620.63530.39850.3117
purelintansig0.828750.11360.16850.1184
logsiglogsig0.838310.25050.25020.1884
tansiglogsig0.853050.25360.25180.195
purelinlogsig0.686720.29550.27180.2067

Influence of hidden neurons of RBF-ANN_

Spread valueNeuronsMSEMSNERMSEMAE
0.11400.998990.000730.01350.0075
0.31400.997420.00190.02150.0108
0.51400.994770.00380.03060.014

0.11300.99730.00190.0220.0141
0.31300.992570.00530.03650.0181
0.51300.992720.00520.03610.0177

0.11200.99360.00460.03390.02
0.31200.988750.00810.04490.0268
0.51200.988330.00840.04570.0266
Language: English
Page range: 1 - 9
Submitted on: Jul 18, 2024
Accepted on: Jan 8, 2025
Published on: Feb 24, 2025
Published by: Slovak Academy of Sciences, Institute of Measurement Science
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2025 Neven Kanchev, Nikolay Stoyanov, Georgi Milushev, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.